Finite Group Databasebeta

← #14775151

Subgroups — #14775151

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2#13071654C211yesmaximal, characteristic
3#13071509C211yesmaximal, characteristic, complemented
4#13069358C211yesmaximal, characteristic, complemented
5#13069314C211yesmaximal, characteristic, complemented
6#13069234C211yesmaximal, characteristic, complemented
7#13069204C211yesmaximal, characteristic, complemented
8#13069185C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068878C211yesmaximal, characteristic, complemented
11#13068815C211yesmaximal, characteristic, complemented
12#13068512C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C11×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28#10622616C418yescomplemented
29#10622601C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622570—21no—
43#10622569—21no—
44#10622564—21no—
45#10622564—21no—
46#10622553—21no—
47C4×(C2×D11)⋊C4—21no—
48#10622550—21no—
49C4×C4⋊Dic11—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C8×C11—22no—
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—41no—
72C11×#117C2×C414yescomplemented
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84#66983—22no—
85#66983C2×C414yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66946—22no—
104#66946—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C22⋊(C11⋊C8)C2×C414yescomplemented
115#66885—22no—
116#66885—41no—
117#66879—22no—
118#66879—41no—
119#66873C2×C414yes—
120#66873C2×C414yes—
121#66872—22no—
122#66872C2×C414yescomplemented
123#66871—41no—
124#66871C2×C414yescomplemented
125#22933—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C23×D11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11C22×C412yes—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—81no—
142C2×C22⋊D11—81no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C22×C412yes—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—44no—
165C2×C8×C11#4112yes—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4C22×C412yes—
173C11×C4⋊C4#4112yes—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—42no—
176C42×C11—24no—
177C42×C11—42no—
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11—81no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—81no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11C22×C412yes—
193Dic11⋊C4—81no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—81no—
199C4×Dic11—81no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8C22×C412yes—
206C2×C11⋊C8C22×C412yes—
207C2×#482—111no—
208#2363—111no—
209#2347—111no—
210#1944—111no—
211#1936—111no—
212#1925—111no—
213#1920—111no—
214#1918—111no—
215#1893—111no—
216#1864—111no—
217#1854—111no—
218#1776—111no—
219#1762—111no—
220#1752—111no—
221#1735D1111yescharacteristic, complemented
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11C4×D412yes—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11C4×D412yes—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C22⋊D11—84no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284D44—22no—
285D44—22no—
286D44—41no—
287D44—41no—
288C4×D11—84no—
289C8×C11—22no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—22no—
293C23×C8C2×D1111yescharacteristic
294C2×#121—111no—
295C2×C4×D4—111no—
296C2×#117C2×D1111yescharacteristic
297C2×#117C2×D1111yescharacteristic
298#482—118no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#106—111no—
302C2×#106—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×C22⋊C8—111no—
308C2×#97—111no—
309C2×#97—111no—
310#390—111no—
311#390—221no—
312#389—111no—
313#389—111no—
314#389—111no—
315#388—221no—
316#388—221no—
317#388—221no—
318#386—221no—
319#383—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—221no—
325C4×C22⋊C4—111no—
326C4×C22⋊C4—221no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332#340C2×D1111yescharacteristic
333#340C2×D1111yescharacteristic
334#340C2×D1111yescharacteristic
335#336—111no—
336#336—111no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C22×C11#54611yescharacteristic
346C22×C11#54711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57511yescharacteristic
349C22×C11#57611yescharacteristic
350C22×C11#57711yescharacteristic
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C4×C11—22no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11C4×#4111yescharacteristic
364C4×C11#52011yescharacteristic
365C4×C11#55111yescharacteristic
366C4×C11#55211yescharacteristic
367Dic11—41no—
368Dic11—41no—
369Dic11—42no—
370Dic11—41no—
371Dic11—41no—
372Dic11—81no—
373Dic11—81no—
374C22×D4—111no—
375C22×D4—221no—
376C23×C4—221no—
377C23×C4C22×D1111yescharacteristic
378C22×C8—22no—
379C22×C8—22no—
380C22×C8—41no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#121—114no—
386#121—222no—
387C4×D4—222no—
388C4×D4—441no—
389#117—22no—
390#117—22no—
391#117—41no—
392#117C4×D1114yescomplemented
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419#107—114no—
420#107—441no—
421#106—114no—
422#106—222no—
423#102—114no—
424#102—114no—
425#102—222no—
426#102—441no—
427C22⋊C8—114no—
428#97—222no—
429#97—441no—
430#95—111no—
431#95—111no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—42no—
440C2×C11#235911yescharacteristic
441C2×C11#294311yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11#330911yescharacteristic
444C2×C11#331111yescharacteristic
445C2×C11#334711yescharacteristic
446C2×C11#335011yescharacteristic
447D11—82no—
448C24—221no—
449C24D4×D1111yescharacteristic
450C2×D4—112no—
451C2×D4—224no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—881no—
458C2×D4—881no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—881no—
477C22×C4C2×C4×D1112yes—
478C22×C4D4×D1111yescharacteristic
479C22×C4#434112yes—
480C22×C4C23×D1111yescharacteristic
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—44no—
487C2×C8—112no—
488C2×C8—112no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8#433912yes—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—112no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—881no—
508C4⋊C4C2×C4×D1112yes—
509C4⋊C4C2×C4×D1112yes—
510C4⋊C4#433912yes—
511C22⋊C4—24no—
512C22⋊C4—42no—
513C22⋊C4—224no—
514C22⋊C4—442no—
515C22⋊C4—442no—
516C22⋊C4—441no—
517C22⋊C4—441no—
518C22⋊C4—881no—
519C22⋊C4—881no—
520C42—24no—
521C42—42no—
522C42—221no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42—881no—
527C42—881no—
528C42—881no—
529C11#2293311yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—222no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23(C22⋊D11)⋊C412yes—
544C23C2×D4×D1111yescharacteristic
545D4—222no—
546D4—222no—
547D4—441no—
548D4—441no—
549D4—884no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—222no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4(C22⋊D11)⋊C412yes—
591C2×C4C22×C4×D1111yescharacteristic
592C2×C4C2×#433911yescharacteristic
593C2×C4C2×#433911yescharacteristic
594C2×C4C2×#434111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4#6704011yescharacteristic
597C8—22no—
598C8—41no—
599C8—222no—
600C8—222no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22C2×(C22⋊D11)⋊C411yescharacteristic
616C22#1062302111yescharacteristic
617C22#1062303811yescharacteristic
618C22#1062329911yescharacteristic
619C22#1062329911yescharacteristic
620C22#1062330011yescharacteristic
621C22#1062330111yescharacteristic
622C4—22no—
623C4—42no—
624C4—42no—
625C4—42no—
626C4—81no—
627C4—441no—
628C4—441no—
629C4—441no—
630C4—441no—
631C4—442no—
632C4—881no—
633C4—881no—
634C4C4×#433911yescharacteristic
635C4#1062302611yescharacteristic
636C4#1062303511yescharacteristic
637C4#1062304411yescharacteristic
638C2—42no—
639C2—882no—
640C2#1307160411yescharacteristic
641C2#1307741211yescharacteristic
642C2#1307745111yescharacteristic
643C2#1308061811yescharacteristic
644C2#1308064811yescharacteristic
645C2#1308111211yescharacteristic
646C2#1308115711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1735D11
hypocenterC11#22933
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #13071509C2semidirect
4. #13069358C2semidirect
5. #13069314C2semidirect
6. #13069234C2semidirect
7. #13069204C2semidirect
8. #13069185C2semidirect
10. #13068878C2semidirect
11. #13068815C2semidirect
12. #13068512C2semidirect
13. #13068440C2semidirect
14. #13068392C2semidirect
15. C11×#1735C2semidirect
28. #10622616C4semidirect
72. C11×#117C2×C4semidirect
114. C22⋊(C11⋊C8)C2×C4semidirect
122. #66872C2×C4semidirect
124. #66871C2×C4semidirect
221. #1735D11semidirect
392. #117C4×D11semidirect
529. C11#22933semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106226162
#130716542
#130715092
#130693582
#130693142
#130692342
#130692042
#130691852
#130690442
#130688782
#130688152
#130685122
#130684402
#130683922
C11×#17352
#2293311